NQueens Problem with CUDA

Transcription

1 NQueens Prblem with CUDA Shuqing Chen ( ) [MAP] [S.Chen] [NQueens Prblem with CUDA]

2 Table f Cntents Backgrund Apprach Evaluatin Discussin Cnclusin [MAP] [S.Chen] [NQueens Prblem with CUDA]

3 Backgrund The NQueens Prblem: Prblem f placing N nnattacking queens n an NxN chessbard. Cnstraints: nly ne queen in each rw, each clumn, r each diagnal. Typical Algrithmus: Backtracking Using backtracking t slute eight-queens (Quelle: Wikipedia) [MAP] [S.Chen] [NQueens Prblem with CUDA]

4 Backgrund Related wrk: The slutin cunt fr N>26 is still unknwn. Slutin cunts (Quelle: Wikipedia) [MAP] [S.Chen] [NQueens Prblem with CUDA]

5 Backgrund Related wrk: By N=26, 9 mnths ( QUEENS@TUD prject) Cmputatin time f Jeff Smer s implementatin with C n CPU [MAP] [S.Chen] [NQueens Prblem with CUDA]

6 Apprach with CUDA - Analysis Advantages f GPU: Efficiently lauching lts f threads Running lts f threads in parallel Prperties f CUDA: Cmputing cherence: All threads execute the same lgic => avid switch Lw perfrmance by recursin [MAP] [S.Chen] [NQueens Prblem with CUDA]

7 Apprach with CUDA - Parallelziatin General Idea: If the queen is n the edge, the number f pssible psitin fr the queen in the next rw is N-2. If the queen is in the middle, the number f pssible psitin fr the queen in the next rw is N-3. If result f 2nd rw is X, the 3rd rw is X-3 r X-2 r X-1. N(N-1)(N-2)...1, N! states, N! threads Blck dimensin: N! -> thread index 3D: t prvide a larger N (limit e.g x x 65535) [MAP] [S.Chen] [NQueens Prblem with CUDA]

8 Apprach with CUDA: Kernel: calculate and verify each pssible state in kernel Parse queen distributin Validate distributin f clumn: Recnstruct index Validate Verify diagnal Alternative Algrithmus: Reference cde frm Ping-Che Chen et al. (Backtracking + depth first search) Reference cde frm Sascha Rlff (Backtracking ) [MAP] [S.Chen] [NQueens Prblem with CUDA]

9 Apprach with CUDA - Evaluatin: Results fr N<9: CPU J.Smer <1ms 70 Cmputatin Time fr N< Time(ms) Native PCChen Sascha [MAP] [S.Chen] [NQueens Prblem with CUDA]

10 Apprach with CUDA - Evaluatin: Results fr N=12, N=13 : Cmputatin Time fr N=12, N= Time(s) Native PCChen CPU JSmer [MAP] [S.Chen] [NQueens Prblem with CUDA]

11 Apprach with CUDA - Evaluatin: Cmputatin time f native implementatin n different testing platfrms: Graphic card NVIDIA Quadr 3000M 2048MB NVIDIA GeFrce GT 650M 512MB NVIDIA GeFrce 610M 1024MB Cre 240 (5x48) 384 (2x192) max. Threads/ Prcessr GPU Clck BUS Width N=9 (ms) N=10 (ms) N=11 (ms) GHz 256bit MHz 128bit (1x48) GHz 64bit [MAP] [S.Chen] [NQueens Prblem with CUDA]

12 Apprach with CUDA - Discussin: Advantages: N recursin, n functin call Lw usage f memry Effentient by small N (N<10) Bttleneck: Lw perfrmance by large N Large number f threads => Max. N depends n the GPU Optimizatin: Shared memry: nt better here Bitmask: demand f large memry by large N [MAP] [S.Chen] [NQueens Prblem with CUDA]

13 Apprach with CUDA - Discussin: Pssible ptimizatin: D(n) n! c n with c 0.39 (Reference: [1]), N! -> 0.39 n N! OR N! -> N*(N-2)*... Challenge: Allcate the queens by using thread index Partitin the prblem int sub-prblems (Reference:[9]) Challenge: Validatin by cmbining Other pssibilities: Algrithms: e.g. Depth-first N 4 (Reference:[4]) Precalculated bard setting (Reference:[8]) [MAP] [S.Chen] [NQueens Prblem with CUDA]

14 Apprach with CUDA: Anther Study Vitr Pamplna: n-queens Prblem: A Cmparisin between CPU and GPU using C++ and CUDA [MAP] [S.Chen] [NQueens Prblem with CUDA]

15 Apprach with CUDA - Cnclusin: Cnclusin f NQueens with CUDA: CUDA is nt always efficient Perfrmance depends n implementatin Challenges f NQueens with CUDA: Parallizatin Allcate queens by using thread index Mathematic & Algrithms [MAP] [S.Chen] [NQueens Prblem with CUDA]

16 Thank yu fr yur attentin! References: 1. Wikipedia 2. Udacity: Intrductin t Parallel Prgramming 3. Nvidia, Nvidia CUDA - Prgramming Guide 4. V. Pamplna. (2008) n-queens Prblem: A Cmparisn Between CPU and GPU using C++ and Cuda (Presentatin). Universidade Federal d Ri Grande d Sul. 5. Cde frm Ping-Che Chen et al.: v2.x/benchmarks/cuda/nqu?rev=aa279fb1aac88a6cad13c7d901782a4bbae4e8d0 6. Cde frm Sascha Rlff 7. Implementatin frm Jeff Smer: 8. F. Feinbube et al.: NQueens n CUDA: Optimizatin Issues 9. T.Zhang et al.: Qptimizatin f N-Queens Slvers n Graphics Prcessrs [MAP] [S.Chen] [NQueens Prblem with CUDA]